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Easy Decision Diffie-Hellman Groups

Published online by Cambridge University Press:  01 February 2010

Steven D. Galbraith  and
Victor Rotger
Steven D. Galbraith
Affiliation:
Mathematics Department, Royal Holloway University of London, Egham. Surrey TW20 OEX, United Kingdom, Steven.Galbraith@rhul.ac.uk, http://www.isg.rhul.ac.uk/~sdg/
Victor Rotger
Affiliation:
Universitat Politècnica de Catalunya, Departament de Matemàtica Aplicada IV (EUPVG), Av. Victor Balaguer s/n 08800 Vilanova i la Geltrú, Spain, vrotger@mat.upc.es

Abstract

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The decision Diffie-Hellman problem (DDH) is a central computational problem in cryptography. It is known that the Weil and Tate pairings can be used to solve many DDH problems on elliptic curves. Distortion maps are an important tool for solving DDH problems using pairings, and it is known that distortion maps exist for all super-singular elliptic curves. An algorithm is presented here to construct suitable distortion maps. The algorithm is efficient on the curves that are usable in practice, and hence all DDH problems on these curves are easy. The issue of which DDH problems on ordinary curves are easy is also discussed.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 7 , 2004 , pp. 201 - 218
Copyright
Copyright © London Mathematical Society 2004

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